Problem: Solve for $x$ and $y$ using elimination. ${-4x+2y = 2}$ ${3x-2y = -4}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-x = -2$ $\dfrac{-x}{{-1}} = \dfrac{-2}{{-1}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-4x+2y = 2}\thinspace$ to find $y$ ${-4}{(2)}{ + 2y = 2}$ $-8+2y = 2$ $-8{+8} + 2y = 2{+8}$ $2y = 10$ $\dfrac{2y}{{2}} = \dfrac{10}{{2}}$ ${y = 5}$ You can also plug ${x = 2}$ into $\thinspace {3x-2y = -4}\thinspace$ and get the same answer for $y$ : ${3}{(2)}{ - 2y = -4}$ ${y = 5}$